Pythagoras Theorem Application

Introduction The Pythagorean Theorem is one of the most useful formulas in mathematics because there are so many applications of it in out in the world. Some examples: Architects and engineers use this formula extensively when building ramps Painting on a Wall Crossing the pond in shortest way Constructing a tent

Example 1: To avoid a pond, vinod walked from point A to 34 meters south point B and then 41 meters east to point C.  Find how many meters it would have taken for vinod if he had went from point A to Point B Solution Given: AC=34m,CB=41m. To find: AB AB2 = AC2 + CB2 (Pythagorean theorem) AB2 = 342 + 412 = 1156 + 1681 AB2 = 2837 Ans:- It would have taken vinod 53.26m to walk from point A to point B

Example 2: Oscar's dog house is shaped like a tent Example 2: Oscar's dog house is shaped like a tent.  The slanted sides are both 5 m long and the bottom of the house is 6 m across.  What is the height of his dog house, in feet, at its tallest point? Solution Given: AC=5M , AB=5 m, BD=3m ,DC=3m To find: AD AC2 = AD2 + DC2 (Pythagorean theorem) AD2 = AC2 - DC2 AD2 = 52 – 32 AD2 = 25 – 9 AD2 = 16 Ans:- The height of dogs house is 4m

from the base of the wall? Example3: How far up a wall will an 11m ladder reach, if the foot of the ladder must be 4m from the base of the wall? Solution: From the diagram, This figure has been restructured as ∆ABC Given: AC=11m, BC=4m To find: AB AC2 = AB2 + BC2 (Pythagorean theorem) AB2 = AC2 - BC2 AB2 = 112 – 42 AB2 = 121 – 16 AB2 = 105 Ans:- The ladder will reach 10.24 m in height

Try These A 24 m long ladder reached a window 25m high from the ground. On placing it against a wall at a distance x m. Find x. A rectangular field is of dimension 40m by 30m. What distance is saved by walking diagonally across the field?